Question

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Answer 1

Answer:

$\textsf {1. x = 28}$

$\textsf {2. a = c = e = f = 55 and b = d = 125}$

Step-by-step explanation:

$\textsf {Question 1}$

$\textsf {Here, the Angle Sum Property needs to be remembered, }\\\textsf {which states that the internal angle sum of a triangle is }\\\textsf {equal to 180 degrees.}$

$\textsf {Solving :}$

$\implies \mathsf {5x - 60 + 2x + 40 + 3x - 80 = 180}$

$\implies \mathsf {10x - 100 = 180}$

$\implies \mathsf {10x = 280}$

$\implies \mathsf {x = \frac{280}{10}}$

$\implies \mathsf {x = 28}$

$\textsf {Question 2}$

$\textsf {Now, remember the sum of linear angles is 180,}\\ \textsf{vertical angles are equal, and corresponding angles are equal.}$

$\textsf {Hence, e = f = a = c = 180 - 125}$

$\implies \mathsf {a = c = e = f = 55}$

$\textsf {Also, b and d are equal to the listed angle as}\\ \textsf{d corresponds to it, and b is the vertical angle of d. }$

$\implies \mathsf {b = d = 125}$

Answer 2

$\star\:{\underline{\underline{\sf{\purple{ \: Question \: 1\: }}}}}$

${\large{\textsf{\textbf{\underline{\underline{Given \: :}}}}}}$

‣ Angle A = 5x - 60°

‣ Angle B = 2x + 40°

‣ Angle C = 3x - 80°

${\large{\textsf{\textbf{\underline{\underline{To \: Find \: :}}}}}}$

‣ The value of $x$

${\large{\textsf{\textbf{\underline{\underline{Solution \: :}}}}}}$

By angle sum property [ASP] of a triangle which states that the sum of all angles of a triangle = 180°

$\longrightarrow \tt A+B+C =180°$

$\longrightarrow \tt (5x - 60) + (2x + 40) + (3x - 80) =180$

$\longrightarrow \tt 5x + 2x + 3x - 60 + 40 - 80 =180$

$\longrightarrow \tt 10x - 60 + 40 - 80 =180$

$\longrightarrow \tt 10x - 140 + 40 =180$

$\longrightarrow \tt 10x - 100 = 180$

$\longrightarrow \tt 10x = 180 + 100$

$\longrightarrow \tt x = \cancel{\dfrac{280}{10} }$

$\longrightarrow \tt x = \purple{28 \degree}$

Therefore, the value of $x$ is 28°

$\star\:{\underline{\underline{\sf{\red{ \: Question \: 2\: }}}}}$

${\large{\textsf{\textbf{\underline{\underline{Given \: :}}}}}}$

‣ Line p is parallel to line q which is intersected by a transversal.

${\large{\textsf{\textbf{\underline{\underline{To \: Find \: :}}}}}}$

‣ The unknown angles.

${\large{\textsf{\textbf{\underline{\underline{Solution \: :}}}}}}$

Finding angle $e$

[linear pair axiom]

$\longrightarrow \tt 125 \degree + \angle e = 180 \degree$

$\longrightarrow \tt \angle e = 180 \degree - 125 \degree$

$\longrightarrow \tt \angle e = \red{55 \degree}$

Now,

For angle $f$

[Vertically opposite angles]

$\longrightarrow \tt \angle f = \angle e$

$\longrightarrow \tt \angle f = \green{55 \degree }$

Now,

For angle $a$

[Corresponding angles]

$\longrightarrow \tt \angle a = \angle e$

$\longrightarrow \tt \angle a = \orange{55 \degree}$

Now,

For angle $d$

[Corresponding angles]

$\longrightarrow \tt \angle d = \pink{125 \degree}$

Now,

For angle $c$

[Vertically opposite angles]

$\longrightarrow \tt \angle c = \angle a$

$\longrightarrow \tt \angle c = \gray{ 55 \degree}$

Now,

For angle $b$

[Vertically opposite angles]

$\longrightarrow \tt \angle b = \angle d$

$\longrightarrow \tt \angle b = \purple{ 125 \degree}$

Hence,

★ Angle A = 55°

★ Angle B = 125°

★ Angle C = 55°

★ Angle D = 125°

★ Angle E = 55°

★ Angle F = 55°

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